Signal Processing and Linear Systems-B.P.Lathi copy

B etween samples t he f requency response especially

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Unformatted text preview: a n LTID system with transfer function H[z] t o a n everlasting sinusoid o f frequency n is also a n everlasting sinusoid of t he s ame frequency. T he o utput amplitUde is IH [ein]1 t imes t he i nput a mplitude, a nd t he o utput sinusoid is shifted in phase with respect to t he i nput sinusoid by L H[e in ] r adians. T he p lot of IH[einli vs n indicates t he a mplitude gain of sinusoids of various frequencies a nd is called t he a mplitude response of t he system. T he p lot o f L H [e in ] vs n indicates t he p hase shift of sinusoids of various frequencies a nd is called t he p hase response. T he frequency response of a n LTID system is a periodic function o f n w ith period 21r. T his periodicity is t he result of t he fact t hat d iscrete-time sinusoids w ith frequencies differing by an integral multiple of 21r a re identical. Frequency response of a system is determined by locations in t he complex plane o f poles a nd zeros of its transfer function. We can design frequency selective filters by G 12 Frequency Response a nd D igital F ilters 778 p roper p lacement of its transfer function poles a nd zeros. Placing a pole (or a zero) n ear t he p oint e jflo i n t he c omplex plane enhances (or suppresses) t he f requency r esponse a t t he frequency n = no. Using this concept, a p roper c ombination o f p oles a nd zeros a t s uitable locations c an yield desired filter characteristics. Digital filters are classified i nto recursive a nd n onrecursive filters. T he d uration o f t he impulse response of a recursive filter is infinite; t hat o f t he nonrecursive filter is finite. For t his reason, recursive filters are also called infinite impulse response ( IIR) filters, a nd nonrecursive filters are called finite impulse response ( FIR) filters. Digital filters c an process analog signals using A ID a nd D I A converters. P rocedures for designing a digital filter t hat behaves like a given analog filter a re discussed. A digital filter can simulate t he b ehavior o f a given analog filter e ither i n time-domain o r i n frequency-domain. This s ituation l eads t o two different design procedures, one using a time-domain equivalence criterion a nd t he o ther a f requency-domain equivalence criterion. For recursive or I IR filters, t he t ime-domain equivalence criterion yields t he i mpulse invariance method, a nd t he frequency-domain equivalence criterion yields t he bilinear t ransformation m ethod. T he impulse invariance m ethod is h andicapped b y t he aliasing problem, a nd c annot b e used for highpass a nd b andstop filters. T he bilinear t ransformation m ethod, which is generally superior t o t he i mpulse invariance m ethod, suffers from t he frequency scale warping effect. However, t his effect can be neutralized by prewarping. For nonrecursive or F IR filters, t he t ime-domain equivalence criterion leads t o t he m ethod of windowing (Fourier series method), a nd t he f requency-domain equivalence criterion leads t o t he m ethod o f frequency sampling. Because nonrecursive filters are a speci...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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